Abstract: Using the modular invariance of the torus, constraints on the 1D patterns arederived that are associated with various fractional quantum Hall ground states,e.g. through the thin torus limit. In the simplest case, these constraintsenforce the well known odd-denominator rule, which is seen to be a necessaryproperty of all 1D patterns associated to quantum Hall states with minimumtorus degeneracy. However, the same constraints also have implications for thenon-Abelian states possible within this framework. In simple cases, includingthe $ u=1$ Moore-Read state and the $ u=3-2$ level 3 Read-Rezayi state, thefilling factor and the torus degeneracy uniquely specify the possible patterns,and thus all physical properties that are encoded in them. It is also shownthat some states, such as the -strong p-wave pairing state-, cannot inprinciple be described through patterns.